A Linear-Scaling Divide-and-Conquer Quantum Chemical Method for Open-Shell Systems and Excited States

Takeshi Yoshikawa*, Hiromi Nakai

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

6 Citations (Scopus)


The acceleration of ab initio electronic structure calculations has been one of the most important themes in the field of quantum chemistry since the mid-1980s when a series of single-reference theories starting from the Hartree-Fock (HF) method were already mature. The standard single-reference quantum chemical calculations consist of three time-consuming steps, namely, the Fock-matrix construction, its diagonalization to obtain the molecular orbitals (MOs) and/or one-electron density matrix, and the post-HF correlation calculation that does not appear in the HF and Kohn-Sham (KS) density functional theory (DFT) calculations. This chapter reviews the linear-scaling quantum chemical calculation for the extension to open-shell and excited-state theories based on the divide-and-conquer (DC) method. Finally, it describes the efficiencies of the DC-UHF and UMP2 methods in measuring the central processing unit (CPU) time. The performance of the present DC-CIS, DC-TDDFT, and DC-SACCI methods is numerically assessed by comparing the results with those of conventional CIS, TDDFT, and SACCI calculations.

Original languageEnglish
Title of host publicationFragmentation
Subtitle of host publicationToward Accurate Calculations on Complex Molecular Systems
Number of pages25
ISBN (Electronic)9781119129271
ISBN (Print)9781119129240
Publication statusPublished - 2017 Jun 21


  • DC-UHF method
  • Density functional theory
  • Excited-state theory
  • Hartree-Fock method
  • Linear-scaling divide-and-conquer quantum chemical method
  • Molecular orbitals
  • Open-shell systems
  • Quantum chemistry
  • UMP2 method

ASJC Scopus subject areas

  • General Chemistry


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